Wideband reflection amplification circuit design method based on real frequency matching method

Abstract

The invention discloses a broadband reflection amplification circuit design method based on a real frequency matching method, which comprises the following steps: firstly designing a reflection amplification circuit, designing a real frequency matching network based on the real frequency matching method, and finally inserting the real frequency matching network into the input end of the reflection amplification circuit to construct the broadband reflection amplification circuit based on the real frequency matching method. According to the method, the input impedance of the reverse amplification circuit is tested through the load traction technology, then the parameter characteristics of the matching network are calculated through the optimization algorithm, and finally the structure and parameter values of the matching network are obtained through the circuit synthesis method, so that the method is not limited by a specific matching network architecture, the performance of the matching network can be greatly improved, and the reliability of the matching network is improved. The problem of broadband matching between the transmitting-receiving antenna and the reflection amplification circuit is solved, so that the reflection amplification circuit can realize high gain under different input powers and input frequencies, the working bandwidth of the reflection amplification circuit is expanded, and the purpose of expanding the application scene of the reflection amplification circuit is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of reflection amplification radio frequency circuits, and in particular relates to a broadband reflection amplification circuit design method based on a real frequency matching method. Background Art

[0002] In the application field of the Internet of Things, in order to reduce the power consumption of the terminal, RFID technology based on backscatter communication is often used. Its passive terminal (tag) is self-powered by energy collection, and data is sent by backscattering, without the need to transmit energy, which greatly reduces the power consumption of the terminal. However, the system using backscatter communication has very low reflection power, which greatly limits the communication distance of the system reflection link. To solve this problem, the existing method is to increase the reflection power by using reflection amplification technology, which is mainly based on the negative resistance characteristics of the transistor or the tunnel diode. However, the backscatter circuit has only one port, which is used as both input and output. The communication bandwidth of the reflection amplification system directly realized by the backscatter circuit is very narrow, which seriously affects the application field of the reflection amplification terminal.

[0003] The existing method to improve the bandwidth of the reflection amplifier circuit is to add a matching network to the input of the reverse amplifier circuit. However, the method of using the existing fixed structure to achieve input matching of the reflection amplifier circuit limits the working bandwidth of the system and cannot achieve optimal matching. The existing reflection amplifier circuit adopts the existing fixed matching circuit structure method, and its structure mainly includes L-type, T-type, and π-type. The function of the matching network is to achieve matching between the load impedance and the source impedance, reduce signal reflection, and improve system performance. The existing matching network is used to achieve matching of the reflection amplifier circuit. Due to the diversity of input impedance and load impedance, and the fact that the gain of the reflection amplifier circuit is greatly affected by the frequency and power of the antenna receiving signal, it is difficult for the fixed matching structure to achieve optimal matching in various application situations, which limits the performance of the reflection amplifier circuit.

[0004] In summary, the existing matching network can only select a fixed matching circuit structure, which has poor adaptability and cannot change the circuit architecture according to application requirements. Especially for narrow-band circuits such as reflection amplification, the matching network with a fixed structure is even more difficult to meet actual application requirements. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a broadband reflection amplifier circuit design method based on the real frequency matching method, which adopts load pulling technology to obtain the reflection amplifier input impedance and antenna input impedance under different powers and frequencies, and realizes the optimal matching in various situations through optimization algorithm, so as to achieve the purpose of high gain of the reflection amplifier circuit under different input powers and frequencies.

[0006] The technical solution adopted by the present invention is: a broadband reflection amplifier circuit design method based on real frequency matching method, and the specific steps are as follows:

[0007] S1. Design the reflection amplifier circuit and design the real frequency matching network based on the real frequency matching method;

[0008] First, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and network synthesis method, and the S parameters (S 11 , S 12 , S 21 , S 22 ) is used to characterize the characteristics of the matching network.

[0009] The real frequency matching network includes two ports, port 1 is the input port, and port 2 is the output port; 11 is the reflection coefficient of the matching network input port, S 22 is the reflection coefficient of the matching network output port, S 12 It represents the reflection coefficient from the output port to the input port of the matching network, S 21 It represents the reflection coefficient from the input port to the output port of the matching network.

[0010] Then the S parameter characterization expression of the real frequency matching network is as follows:

[0011]

[0012] Where σ represents a variable, s=jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, h(s), f(s) represent arbitrary real coefficient polynomials, and satisfy the following constraints:

[0013] g(s)g(-s)=f(s)f(-s)+h(s)h(-s) (2)

[0014] The antenna impedance Z in the real frequency matching network is obtained through actual testing in , and then adjust the corresponding value in the S parameter to make the load impedance Z L The impedance value required to transform to the input impedance.

[0015] Port 1 reflection coefficient Γ in The expression is as follows:

[0016]

[0017] Among them, Z s is the source impedance, Z in Indicates input impedance.

[0018] From formula (3) and the definition of S parameters, we can know the relationship between reflection coefficient and S parameters, which is expressed as follows:

[0019] S 11 =Γin (4)

[0020] According to the lossless characteristics of the matching network, S 21 With S 11 The relationship is expressed as follows:

[0021]

[0022] In the process of realizing the matching network, let T0 represent the desired transmission gain, ω i (i=1,2…,n…,N) represents the frequency of each discrete point selected in the working frequency band, and N represents the total number of discrete points selected. The expression of the optimized cost function is as follows:

[0023]

[0024] Wherein, ΔT represents the sum of the squares of the differences between the actual transmission gain and the expected transmission gain at each discrete point, and T represents the current transmission gain.

[0025] After the network function that meets the matching requirements is calculated through the least squares optimization algorithm, the single-port driving point impedance function expression of the load matching network is as follows:

[0026]

[0027] Among them, λ represents a variable, R S represents the impedance of the input source, g(λ) represents the Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial.

[0028] The rational fraction form of formula (7) is as follows:

[0029]

[0030] Where n and m represent the highest power of the numerator and denominator s calculated; a i and b i Represent the coefficients of the numerator and denominator polynomials of the impedance function respectively.

[0031] The cost function expression based on the impedance error function is as follows:

[0032]

[0033] Among them, ΔZ represents the impedance fluctuation value, Z in (ω i ) indicates that the input port is at the frequency point ω i The input impedance, Z opt (ω i ) indicates that at the frequency point ω i The optimal impedance at .

[0034] Finally, the least squares optimization algorithm is used to minimize ΔZ and calculate Z in (ω i ) and then obtain the real-frequency matching network through network synthesis method.

[0035] S2, inserting the real frequency matching network designed in step S1 into the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real frequency matching method;

[0036] The broadband reflection amplifier circuit based on the real frequency matching method comprises: a reflection amplifier circuit, a real frequency matching network, and an antenna; the reflection amplifier circuit is connected to a port 1 of the real frequency matching network, and a port 2 of the real frequency matching network is connected to the antenna.

[0037] Furthermore, in step S1, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and the network synthesis method, as follows:

[0038] A1. Initialize the polynomial h(s), that is, by normalizing the frequency point ω a , the real and imaginary parts of the reflected load, generating the initial value h0 of the polynomial h(s);

[0039] Firstly, load-pull is used to measure the input and output impedance of the reflection amplifier circuit at different frequencies, and then normalized.

[0040] Then, according to the impedance values ​​corresponding to the tested discrete frequency points, the correlation coefficient of the initial value g0 of the denominator polynomial g(s) is calculated as follows:

[0041] Let ω a Indicates the normalized frequency corresponding to the impedance, set the variable x = ω 2 =-s 2 , define the auxiliary polynomial P a (x) The array of linear regression is Xd, that is, Xd = ω a *ω a ′, generate P a The data point set Pd of (x) is calculated as follows:

[0042]

[0043] Among them, ω a ′ represents ω a The conjugate value of S RL and S RX Respectively represent the real and imaginary parts of the impedance value, Pd is P a (x) corresponds to the polynomial coefficients, k represents the total number of DC transmission zeros of the equalizer, and pk represents the kth data point in the data point set Pd.

[0044] Perform polynomial fitting on the data given by Xd and Pd with the selected order nr = n / 2, and use the polyfit function of MATLAB to generate the polynomial P a (x), that is, P a =polyfit(Xd,Pd,nr), then we can get P a (x) = P1x nr +P2x nr-1 +…+P nr+1 The coefficient of .

[0045] Then directly through the MATLAB function G = conv (P a ,P a ) Generate a strictly positive polynomial G(x)=P a 2 (x)>0, get P a (x) The convolution result vector G corresponding to each coefficient.

[0046] Then through the MATLAB function X r =roots(G) to find G(x)=P a 2 (x)>0 root and set the intermediate variable Through the MATLAB function P r =sqrt(-X r ) First generate the right half plane root RHP; then set the intermediate variable P r m=-P r Find the left half plane LHP roots and construct the polynomial g(s) from them.

[0047] Finally, based on the LHP root P r m, through the MATLAB function C = poly(P r m) Construct the polynomial C(s), and then pass Get the vector g0.

[0048] After calculating g0, use MATLAB's polyfit function to generate polynomials A(x) and B(x), and get the polynomial coefficients A d and B d , as follows:

[0049] Let S RLa and S RXa Represents the real and imaginary parts of the load impedance obtained after normalization. For each sampling frequency ω i , let S RL =S RLa (ω i ) and S RX =S RXa (ωi ), then we can get A d (ω i ) = g R *S RL +g X *S RX and B d (ω i )=(g X *S RL +g R *S RX ) / ω.

[0050] Among them, g R , g X That is, g0 is the intermediate variable obtained by the MATLAB function polyval(g0,s), and ω represents ω a At frequency ω i The value of ω=ω a (ω i ).

[0051] Then use the MATLAB function A=polyfit(Xd,A d ,na) and B = polyfit(Xd,B d ,nb) Find the polynomials A(x) and B(x).

[0052] Among them, if the given n is an even number, na=n / 2, nb=(n-2) / 2; if n is an odd number, na=nb=(n-1) / 2.

[0053] Finally, the initial value h0 of the polynomial h(s) is calculated, and the calculation expression is as follows:

[0054] h(s)=A(-s 2 )+sB(s 2 ) (11)

[0055] A2, based on step A1, using nonlinear least squares coefficients to optimize the polynomial h(s);

[0056] Call MATLAB's lsqnonlin function and iterate multiple times to calculate all the optimization coefficients of the polynomial h(s). The expression is as follows:

[0057]

[0058] Among them, ε nopt Represents the minimum error of the nth discrete point optimization.

[0059] Then solve the optimization target, first set the unknown vector x = [.] and set the coefficient vector h = x, assign h0 obtained in step A1 to vector x;

[0060] Get the value g of the polynomial g(s) and h(s) at a given point s val and h val , the normalized value of the driving point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ).

[0061] Based on formula (9), the lsqnonlin function is called to minimize the cost function value, the optimization vector x is obtained, and finally the optimal polynomial h(s) is generated.

[0062] A3. Based on step A2, generate a strict Hurwitz polynomial g(s);

[0063] Based on the optimal polynomial h(s) generated in step A2, let U = [h n h n-1 ...h0], V=[(-1) n h n (-1) n- 1 h n-1 ...h0], the convolution of U and V can be expressed as follows:

[0064] H(-s 2 )=h(s)h(-s)=H0+H1s+...+H n s n (13)

[0065] Among them, h n Represents the coefficient corresponding to the nth discrete point, H n Indicates H(-s 2 )The coefficients corresponding to each item.

[0066] Then generate an even-degree polynomial G(-s 2 ), the expression is as follows:

[0067] G(-s 2 )=H(-s 2 )+(-1) k s 2k =G0+G1s 2 +...+G n s 2n (14)

[0068] Among them, G n Indicates G(-s 2 )The coefficients corresponding to each item, k represents the variable, that is, the coefficient between 0 and n.

[0069] Then store the row vector X, the expression is as follows:

[0070] X=[(-1) n G n (-1) n-1 G n-1 ...G0] (15)

[0071] Calculate G(-s 2 ) The roots pk and pkm in the right and left half planes are expressed as follows:

[0072] pk=sqrt(-Xk) (16)

[0073] pkm=-pk (17)

[0074] Finally, the first polynomial is generated Through MATLAB function Generates the strict Hurwitz polynomial g(s).

[0075] Where gc = {g n g n-1 ...g0} represents the coefficient of the (n+1)th-order row vector, that is, g(s)=g0+g1s+...+gnsn.

[0076] A4. Based on step A3, calculate the current transmission gain T;

[0077] First, define the complex variable s=jω; j=sqrt(-1), then s=sqrt(-1)*ω.

[0078] Calculate the polynomial g using h and g val =polyval(g,s) and h val =polyval(h,s), find g val =g0s n +g1s n-1 +…+g n-1 s+g n ,h val =h0s n +h1s n-1 +…+h n-1 s+h n .

[0079] Through the input impedance (g val +h val ) / (g val -h val ) obtain the current transmission gain T, through g val =polyval(g,s),h val =polyval(h,s),f val=s k and L 11 =h val / g val , we can get Weight = f val conj(f val )(1-L 11 conj(L 11 )) and D=h val conj(h val )(1+L 11 conj(L 11 ))+f val conj(f val )-2real(L 11 h val conj(g val )), then the transmission gain T = Weight / D can be obtained.

[0080] Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, L 11 Represents the load reflection coefficient.

[0081] A5. Based on steps A1-A4, use a network synthesis method to find the real frequency matching network circuit structure;

[0082] Through the optimized h(s) and g(s) and long division method, the component parameters and starting component types of the matching network are obtained, and the values ​​of each input matching item are calculated by the network synthesis formula (18), and the normalized input matching device values ​​are obtained.

[0083]

[0084] Among them, Z L represents the load impedance, X ns Indicates margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, and inductance C n Represents the capacitance at the nth discrete point, L n Represents the inductance at the nth discrete point.

[0085] Finally, based on the tested impedance of the reflection amplifier circuit, the optimal matching network characteristics are calculated, and the corresponding matching circuit is synthesized to design a broadband reflection amplifier circuit.

[0086] Beneficial effects of the present invention: The method of the present invention first designs a reflection amplifier circuit, and designs a real frequency matching network based on a real frequency matching method, and finally inserts a real frequency matching network at the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real frequency matching method. The method of the present invention tests the input impedance of the reverse amplifier circuit by load-pull technology, and then uses an optimization algorithm to calculate the parameter characteristics of the matching network, and finally obtains the structure and parameter values ​​of the matching network by a circuit synthesis method, which is not limited by a specific matching network architecture, can greatly improve the performance of the matching network, solves the broadband matching problem between the transceiver antenna and the reflection amplifier circuit, and enables the reflection amplifier circuit to achieve high gain at different input powers and input frequencies, thereby broadening the working bandwidth of the reflection amplifier circuit and achieving the purpose of expanding the application scenarios of the reflection amplifier circuit.

[0087] Instruction Manual

[0088] Figure 1 The present invention is a flow chart of a method for designing a broadband reflection amplifier circuit based on a real frequency matching method.

[0089] Figure 2 4 is a structural diagram of a broadband reflection amplifier circuit based on a real frequency matching method in an embodiment of the present invention.

[0090] Figure 3 It is a schematic diagram of using S parameters to characterize the characteristics of a matching network in an embodiment of the present invention.

[0091] Figure 4 The figure is a flow chart of the least squares optimization algorithm and the network synthesis method in the embodiment of the present invention. DETAILED DESCRIPTION

[0092] The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0093] like Figure 1 As shown, a flow chart of a broadband reflection amplifier circuit design method based on a real frequency matching method of the present invention, the specific steps are as follows:

[0094] S1. Design the reflection amplifier circuit and design the real frequency matching network based on the real frequency matching method;

[0095] This embodiment proposes a broadband reflection amplifier circuit structure based on the real frequency matching method. Figure 2 As shown in the figure, the real frequency matching network is used to achieve the optimal matching between the reflection amplifier circuit and the antenna under different powers and frequencies. First, the circuit structure of the real frequency matching network is obtained according to the least squares optimization algorithm and the network synthesis method, and the S parameters (S 11 , S 12 , S 21 , S 22 ) is used to characterize the characteristics of the matching network. Figure 3 The S parameters shown are used to characterize the characteristics of the matching network.

[0096] The real frequency matching network includes two ports, port 1 is the input port, and port 2 is the output port; 11 is the reflection coefficient of the matching network input port, S 22 is the reflection coefficient of the matching network output port, S 12 It represents the reflection coefficient from the output port to the input port of the matching network, S 21 It represents the reflection coefficient from the input port to the output port of the matching network.

[0097] Then the S parameter characterization expression of the real frequency matching network is as follows:

[0098]

[0099] Where σ represents a variable, s=jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, h(s), f(s) represent arbitrary real coefficient polynomials, and satisfy the following constraints:

[0100] g(s)g(-s)=f(s)f(-s)+h(s)h(-s) (2)

[0101] The antenna impedance Z in the real frequency matching network is obtained through actual testing in , and then adjust the corresponding value in the S parameter to make the load impedance Z L The impedance value required to transform to the input impedance.

[0102] Depend on Figure 3 It can be seen that the reflection coefficient of port 1 is Γ in The expression is as follows:

[0103]

[0104] Among them, Z s is the source impedance, Z in Indicates input impedance.

[0105] From formula (3) and the definition of S parameters, we can know the relationship between reflection coefficient and S parameters, which is expressed as follows:

[0106] S 11 =Γ in (4)

[0107] According to the lossless characteristics of the matching network, S 21 With S 11 The relationship is expressed as follows:

[0108]

[0109] In the real frequency matching method, we only need to optimize S 21 The value of , so that it is larger and flatter within the working frequency band, the better the performance of the designed matching network.

[0110] In the process of realizing the matching network, let T0 represent the desired transmission gain, ω i (i=1,2…,n…,N) represents the frequency of each discrete point selected in the working frequency band, and N represents the total number of discrete points selected. The expression of the optimized cost function is as follows:

[0111]

[0112] Wherein, ΔT represents the sum of the squares of the differences between the actual transmission gain and the expected transmission gain at each discrete point, and T represents the current transmission gain.

[0113] After the network function that meets the matching requirements is calculated through the least squares optimization algorithm, the single-port driving point impedance function expression of the load matching network is as follows:

[0114]

[0115] Among them, λ represents a variable, R S represents the impedance of the input source, g(λ) represents the Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial.

[0116] The rational fraction form of formula (7) is as follows:

[0117]

[0118] Where n and m represent the highest power of the numerator and denominator s calculated; a i and b i Represent the coefficients of the numerator and denominator polynomials of the impedance function respectively.

[0119] The load matching network can then obtain the type (resistance, capacitance and inductance) and value of each component through network synthesis.

[0120] Since S parameters are mainly used for power matching, they cannot reflect the efficiency characteristics of the reflection amplifier circuit, and when considering harmonic impedance, the form of transmission gain cannot reflect the fluctuation of the harmonic matching state. On the other hand, the optimal impedance of each circuit module can be easily obtained according to load pulling, and the error of the impedance function can directly reflect the output power and efficiency of the reflection amplifier circuit. The cost function expression based on the impedance error function is as follows:

[0121]

[0122] Among them, ΔZ represents the impedance fluctuation value, Z in (ω i ) indicates that the input port is at the frequency point ω i The input impedance, Z opt (ω i ) indicates that at the frequency point ω i Of course, the smaller ΔZ is, the smaller the impedance function Z is. in The closer it is to the target impedance function. By optimizing the algorithm to minimize ΔZ, we can find Z in (ω i ) expression, and further through the network synthesis method, the real-frequency matching network can be obtained, and then a reflection amplifier circuit with broadband and high efficiency characteristics can be designed.

[0123] S2, inserting the real frequency matching network designed in step S1 into the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real frequency matching method;

[0124] like Figure 2 , 3 As shown, the broadband reflection amplification circuit based on the real frequency matching method includes: a reflection amplification circuit, a real frequency matching network, and an antenna; the reflection amplification circuit is connected to port 1 of the real frequency matching network, and port 2 of the real frequency matching network is connected to the antenna.

[0125] In the broadband reflection amplifier circuit based on the real frequency matching method, it is necessary to first generate the polynomials h(s) and g(s), then calculate the transmission gain of the actual matching network at each frequency point, and finally comprehensively calculate the component types and coefficients of the matching network.

[0126] like Figure 4 As shown, in this embodiment, in the step S1, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and the network synthesis method, which is as follows:

[0127] A1. Initialize the polynomial h(s), that is, by normalizing the frequency point ω a , the real and imaginary parts of the reflected load, generating the initial value h0 of the polynomial h(s);

[0128] Firstly, load-pull is used to measure the input and output impedance of the reflection amplifier circuit at different frequencies, and then normalized.

[0129] Then, according to the impedance values ​​corresponding to the discrete frequency points tested, the correlation coefficient of the initial value g0 of the denominator polynomial g(s) is calculated as follows:

[0130] Let ω a Indicates the normalized frequency corresponding to the impedance, set the variable x = ω 2 =-s 2 , define the auxiliary polynomial P a(x) The array of linear regression is Xd, that is, Xd = ω a *ω a ′, generate P a The data point set Pd of (x) is calculated as follows:

[0131]

[0132] Among them, ω a ′ represents ω a The conjugate value of S RL and S RX Respectively represent the real and imaginary parts of the impedance value, Pd is P a (x) corresponds to the polynomial coefficients, k represents the total number of DC transmission zeros of the equalizer (set according to actual conditions), and pk represents the kth data point in the data point set Pd.

[0133] Perform polynomial fitting on the data given by Xd and Pd with the selected order nr = n / 2, and use the polyfit function of MATLAB to generate the polynomial P a (x), that is, P a =polyfit(Xd,Pd,nr), then we can get P a (x) = P1x nr +P2x nr-1 +…+P nr+1 The coefficient of .

[0134] Then directly through the MATLAB function G = conv (P a ,P a ) Generate a strictly positive polynomial G(x) = P a 2 (x)>0, get P a (x) The convolution result vector G corresponding to each coefficient.

[0135] Then through the MATLAB function X r =roots(G) to find G(x)=P a 2 (x)>0 root and set the intermediate variable Through the MATLAB function P r =sqrt(-X r ) First generate the right half plane root (RHP); then set the intermediate variable P r m=-P r Find the left half plane (LHP) roots and construct the polynomial g(s) from them.

[0136] Finally, based on the LHP root P rm, through the MATLAB function C = poly(P r m) Construct the polynomial C(s), and then pass Get the vector g0.

[0137] After calculating g0, use MATLAB's polyfit function to generate polynomials A(x) and B(x), and get the polynomial coefficients A d and B d , as follows:

[0138] Let S RLa and S RXa Represents the real and imaginary parts of the load impedance obtained after normalization. For each sampling frequency ω i , let S RL =S RLa (ω i ) and S RX =S RXa (ω i ), then we can get A d (ω i ) = g R *S RL +g X *S RX and B d (ω i )=(g X *S RL +g R *S RX ) / ω.

[0139] Among them, g R , g X That is, g0 is the intermediate variable obtained by the MATLAB function polyval(g0,s), and ω represents ω a At frequency ω i The value of ω=ω a (ω i ).

[0140] Then use the MATLAB function A=polyfit(Xd,A d ,na) and B = polyfit(Xd,B d ,nb) Find the polynomials A(x) and B(x).

[0141] Among them, if the given n is an even number, na=n / 2, nb=(n-2) / 2; if n is an odd number, na=nb=(n-1) / 2.

[0142] Finally, the initial value h0 of the polynomial h(s) is calculated, and the calculation expression is as follows:

[0143] h(s)=A(-s2 )+sB(s 2 ) (11)

[0144] A2, based on step A1, using nonlinear least squares coefficients to optimize the polynomial h(s);

[0145] Call MATLAB's lsqnonlin function and iterate multiple times to calculate all the optimization coefficients of the polynomial h(s). The expression is as follows:

[0146]

[0147] Among them, ε nopt Represents the minimum error of the nth discrete point optimization.

[0148] Then solve the optimization target, first set the unknown vector x = [.] and set the coefficient vector h = x, assign h0 obtained in step A1 to vector x;

[0149] Get the value g of the polynomial g(s) and h(s) at a given point s val and h val , the normalized value of the driving point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ).

[0150] Based on formula (9), the lsqnonlin function is called to minimize the cost function value, the optimization vector x is obtained, and finally the optimal polynomial h(s) is generated.

[0151] A3. Based on step A2, generate a strict Hurwitz polynomial g(s);

[0152] Based on the optimal polynomial h(s) generated in step A2, let U = [h n h n-1 ...h0], V=[(-1) n h n (-1) n- 1 h n-1 ...h0], the convolution of U and V can be expressed as follows:

[0153] H(-s 2 )=h(s)h(-s)=H0+H1s+...+H n s n (13)

[0154] Among them, h n Represents the coefficient corresponding to the nth discrete point, H n Indicates H(-s2 )The coefficients corresponding to each item.

[0155] Then generate an even-degree polynomial G(-s 2 ), the expression is as follows:

[0156] G(-s 2 )=H(-s 2 )+(-1) k s 2k =G0+G1s 2 +...+G n s 2n (14)

[0157] Among them, G n Indicates G(-s 2 )The coefficients corresponding to each item, k represents the variable, that is, the coefficient between 0 and n.

[0158] Then store the row vector X, the expression is as follows:

[0159] X=[(-1) n G n (-1) n-1 G n-1 ...G0] (15)

[0160] Calculate G(-s 2 ) The roots pk and pkm in the right and left half planes are expressed as follows:

[0161] pk=sqrt(-Xk) (16)

[0162] pkm=-pk (17)

[0163] Finally, the first polynomial is generated Through MATLAB function Generates the strict Hurwitz polynomial g(s).

[0164] Where gc = {g n g n-1 ...g0} represents the coefficient of the (n+1)th-order row vector, that is, g(s)=g0+g1s+...+gnsn.

[0165] A4. Based on step A3, calculate the current transmission gain T;

[0166] First, define the complex variable s=jω; j=sqrt(-1), then s=sqrt(-1)*ω.

[0167] Calculate the polynomial g using h and g val =polyval(g,s) and h val=polyval(h,s), find g val =g0s n +g1s n-1 +…+g n-1 s+g n ,h val =h0s n +h1s n-1 +…+h n-1 s+h n .

[0168] Through the input impedance (g val +h val ) / (g val -h val ) obtain the current transmission gain T, through g val =polyval(g,s),h val =polyval(h,s),f val =s k and L 11 =h val / g val , we can get Weight = fvalconj(fval)(1-L 11 conj(L 11 )) and D=h val conj(h val )(1+L 11 conj(L 11 ))+f val conj(f val )-2real(L 11 h val conj(g val )), then the transmission gain T = Weight / D can be obtained.

[0169] Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, L 11 Represents the load reflection coefficient.

[0170] A5. Based on steps A1-A4, use a network synthesis method to find the real frequency matching network circuit structure;

[0171] Through the optimized h(s) and g(s) and long division method, the component parameters and starting component types of the matching network are obtained, and the values ​​of each input matching item are calculated by the network synthesis formula (18), thereby obtaining the normalized input matching device values.

[0172]

[0173] Among them, ZL represents the load impedance, X ns Indicates margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, and inductance C n Represents the capacitance at the nth discrete point, L n Represents the inductance at the nth discrete point.

[0174] Finally, based on the tested impedance of the reflection amplifier circuit, the optimal matching network characteristics are calculated, and the corresponding matching circuit is synthesized to design a broadband reflection amplifier circuit.

[0175] In summary, in order to solve the problem of narrow bandwidth of existing reflection amplifier matching circuits, the method of the present invention proposes a broadband reflection amplifier circuit design method based on the real frequency matching method, which adopts load pulling technology to obtain the reflection amplifier input impedance and antenna input impedance under different powers and frequencies, and achieves the optimal matching in various situations through optimization algorithm. It can be used to solve the broadband matching problem between the transmitting and receiving antennas and the reflection amplifier circuit, so that the reflection amplifier circuit can achieve high gain under different input powers and input frequencies, broaden the working bandwidth of the reflection amplifier circuit, so as to adapt to the application environment of different input powers and frequencies, and achieve the purpose of expanding the application scenarios of the reflection amplifier circuit.

[0176] Those skilled in the art will appreciate that the above embodiments are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A broadband reflection amplifier circuit design method based on real frequency matching method, the specific steps are as follows: S1. Design the reflection amplifier circuit and design the real frequency matching network based on the real frequency matching method; First, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and network synthesis method, and the S parameters (S 11 , S 12 , S 21 , S 22 ) to characterize the characteristics of the matching network; in, The real frequency matching network includes two ports, S 11 is the reflection coefficient of the matching network input port, S 22 is the reflection coefficient of the matching network output port, S 12 It represents the reflection coefficient from the output port to the input port of the matching network, S 21 It represents the reflection coefficient from the input port to the output port of the matching network; Then the S parameter characterization expression of the real frequency matching network is as follows: Where σ represents a variable, s=jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, h(s), f(s) represent arbitrary real coefficient polynomials, and satisfy the following constraints: g(s)g(-s)=f(s)f(-s)+h(s)h(-s) (2) The antenna impedance Z in the real frequency matching network is obtained through actual testing in , and then adjust the corresponding value in the S parameter to make the load impedance Z L The impedance value required to transform to the input impedance; Input port reflection coefficient Γ in The expression is as follows: Among them, Z s is the source impedance, Z in represents input impedance; From formula (3) and the definition of S parameters, we can know the relationship between reflection coefficient and S parameters, which is expressed as follows: S 11 =C in (4) According to the lossless characteristics of the matching network, S 21 With S 11 The relationship is expressed as follows: In the process of realizing the matching network, let T0 represent the desired transmission gain, ω i (i=1,2…,n…,N) represents the frequency of each discrete point selected in the working frequency band, and N represents the total number of discrete points selected. The expression of the optimized cost function is as follows: Wherein, ΔT represents the sum of the squares of the differences between the actual transmission gain and the expected transmission gain at each discrete point, and T represents the current transmission gain; After the network function that meets the matching requirements is calculated through the least squares optimization algorithm, the single-port driving point impedance function expression of the load matching network is as follows: Among them, λ represents a variable, R S represents the impedance of the input source, g(λ) represents the Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial; Then the rational fraction form of formula (7) is as follows: Where n and m represent the highest power of the numerator and denominator s calculated; a i and b i Respectively represent the coefficients of the numerator and denominator polynomials of the impedance function; The cost function expression based on the impedance error function is as follows: Among them, ΔZ represents the impedance fluctuation value, Z in (ω i ) indicates that the input port is at the frequency point ω i The input impedance, Z opt (ω i ) indicates that at the frequency point ω i The optimal impedance at Finally, the least squares optimization algorithm is used to minimize ΔZ and calculate Z in (ω i ) expression, and then obtain the real frequency matching network through the network synthesis method; S2, inserting the real frequency matching network designed in step S1 into the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real frequency matching method; The broadband reflection amplifier circuit based on the real frequency matching method comprises: a reflection amplifier circuit, a real frequency matching network, and an antenna; the reflection amplifier circuit is connected to the input port of the real frequency matching network, and the output port of the real frequency matching network is connected to the antenna.

2. The method for designing a broadband reflection amplifier circuit based on a real frequency matching method according to claim 1, characterized in that: In step S1, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and the network synthesis method, which is specifically as follows: A1. Initialize the polynomial h(s), that is, by normalizing the frequency point ω a , the real and imaginary parts of the reflected load, generating the initial value h0 of the polynomial h(s); Firstly, load-pull is used to measure the input and output impedance of the reflection amplifier circuit at different frequencies, and then normalized. Then, according to the impedance values ​​corresponding to the discrete frequency points tested, the correlation coefficient of the initial value g0 of the denominator polynomial g(s) is calculated as follows: Let ω a Indicates the normalized frequency corresponding to the impedance, set the variable x = ω 2 =-s 2 , define the auxiliary polynomial P a (x) The array of linear regression is Xd, that is, Xd = ω a *ω a ′, generate P a The data point set Pd of (x) is calculated as follows: Among them, ω a ′ represents ω a The conjugate value, S RL and S RX Respectively represent the real and imaginary parts of the impedance value, Pd is P a (x) The corresponding polynomial coefficients, k represents the total number of DC transmission zeros of the equalizer, and pk represents the kth data point in the data point set Pd; Perform polynomial fitting on the data given by Xd and Pd with the selected order nr = n / 2, and use the polyfit function of MATLAB to generate the polynomial P a (x), that is, P a =polyfit(Xd,Pd,nr), then we can get P a (x) = P1x nr +P2x nr-1 +…+P nr+1 The coefficient of Then directly through the MATLAB function G = conv (P a ,P a ) Generate a strictly positive polynomial G(x)=P a 2 (x)>0, get P a (x) The convolution result vector G corresponding to each coefficient; Then through the MATLAB function X r =roots(G) to find G(x)=P a 2 (x)>0 root and set the intermediate variable Through the MATLAB function P r =sqrt(-X r ) First generate the right half plane root RHP; then set the intermediate variable P r m=-P r Find the left half plane LHP root and construct the polynomial g(s) based on it; Finally, based on the LHP root P r m, through the MATLAB function C = poly(P r m) Construct the polynomial C(s), and then pass Get vector g0; After calculating g0, use MATLAB's polyfit function to generate polynomials A(x) and B(x), and get the polynomial coefficients A d and B d , as follows: Let S RLa and S RXa Represents the real and imaginary parts of the load impedance obtained after normalization. For each sampling frequency ω i , let S RL =S RLa (ω i ) and S RX =S RXa (ω i ), then we can get A d (ω i ) = g R *S RL +g X *S RX and B d (ω i )=(g X *S RL +g R *S RX ) / ω; Among them, g R , g X That is, g0 is the intermediate variable obtained by the MATLAB function polyval(g0,s), and ω represents ω a At frequency ω i The value of ω=ω a (ω i ); Then use the MATLAB function A=polyfit(Xd,A d ,na) and B = polyfit(Xd,B d ,nb) Find the polynomials A(x) and B(x); Wherein, if the given n is an even number, na=n / 2, nb=(n-2) / 2; if n is an odd number, na=nb=(n-1) / 2; Finally, the initial value h0 of the polynomial h(s) is calculated, and the calculation expression is as follows: h(s)=A(-s 2 )+sB(s 2 ) (11) A2, based on step A1, using nonlinear least squares coefficients to optimize the polynomial h(s); Call MATLAB's lsqnonlin function and iterate multiple times to calculate all the optimization coefficients of the polynomial h(s). The expression is as follows: Among them, ε nopt Represents the minimum error of the optimization of the nth discrete point; Then solve the optimization target, first set the unknown vector x = [.] and set the coefficient vector h = x, assign h0 obtained in step A1 to vector x; Get the value g of the polynomial g(s) and h(s) at a given point s val and h val , the normalized value of the driving point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ); Based on formula (9), the lsqnonlin function is called to minimize the cost function value, the optimization vector x is obtained, and finally the optimal polynomial h(s) is generated; A3. Based on step A2, generate a strict Hurwitz polynomial g(s); Based on the optimal polynomial h(s) generated in step A2, let U = [h n h n-1 ...h0], V=[(-1) n h n (-1) n-1 h n- 1...h0], the convolution of U and V gives the following expression: H(-s 2 )=h(s)h(-s)=H0+H1s+...+H n s n (13) Among them, h n Represents the coefficient corresponding to the nth discrete point, H n Indicates H(-s 2 )The coefficients corresponding to each item; Then generate an even-degree polynomial G(-s 2 ), the expression is as follows: G(-s 2 )=H(-s 2 )+(-1) k s 2k =G0+G1s 2 +...+G n s 2n (14) Among them, G n Indicates G(-s 2 ) The coefficients corresponding to each item, k represents the variable, that is, the coefficient between 0 and n; Then store the row vector X, the expression is as follows: X=[(-1) n G n (-1) n-1 G n-1 ...G0] (15) Calculate G(-s 2 ) The roots pk and pkm in the right and left half planes are expressed as follows: Finally, the first polynomial is generated Through MATLAB function Generate strict Hurwitz polynomial g(s); Where gc = {g n g n-1 ...g0} represents the (n+1)th order row vector, that is, g(s) = g0+g1s+...+g n s n The coefficient of A4. Based on step A3, calculate the current transmission gain T; First, define the complex variable s = jω; j = sqrt(-1), then s = sqrt(-1)*ω; Calculate the polynomial g using h and g val =polyval(g,s) and h val =polyval(h,s), find g val =g0s n +g1s n-1 +…+g n-1 s+g n ,h val =h0s n +h1s n-1 +…+h n-1 s+h n ; Through the input impedance (g val +h val ) / (g val -h val ) obtain the current transmission gain T, through g val =polyval(g,s),h val =polyval(h,s),f val =s k and L 11 =h val / g val , we can get Weight = f val conj(f val )(1-L 11 conj(L 11 )) and D=h val conj(h val )(1+L 11 conj(L 11 ))+f val conj(f val )-2real(L 11 h val conj(g val )), then we can get the transmission gain T = Weight / D; Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, L 11 represents the load reflection coefficient; A5. Based on steps A1-A4, use a network synthesis method to find the real frequency matching network circuit structure; The component parameters and starting component types of the matching network are obtained by using the optimized h(s) and g(s) and long division method. The values ​​of each input matching item are calculated by the network comprehensive formula (18), and the normalized input matching component values ​​are obtained. Among them, Z L represents the load impedance, X ns Indicates margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, and inductance C n Represents the capacitance at the nth discrete point, L n represents the inductance at the nth discrete point; Finally, based on the tested impedance of the reflection amplifier circuit, the optimal matching network characteristics are calculated, and the corresponding matching circuit is synthesized to design a broadband reflection amplifier circuit.

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